This project will investigate theory, methods and applications of mathematical statistics and probability, with particular emphasis on the problems with data collected by NICHD. Current focus is on 1) the analysis of data arising from longitudinal studies with repeated measurements, 2)nonparametric procedures and the area under the receiver operating characteristic curve, and 3) the testing for disease clustering in communities. Examples of NICHD projects on longitudinal studies are Successive Small-for-Gestational Age Study I and Study II in Alabama and Scandinavia, Preventing Problem Behavior Among Middle School Students and the Longitudinal Study of Vaginal Flora. A host of statistical procedures for estimation and hypothesis testing will be proposed and investigated for the time varying coefficient models via their asymptotic properties and simulations. Applications will be developed to handle questions concerning various issues in perinatal and reproductive epidemiology. Data will be fitted to growth models such as Rossavik model, linear model and logistic model. New and rigorous statistical methods and algorithms will be generated and validated through investigation of their statistical and probabilistic properties. Computer-intensive techniques such as bootstrapping methodology will be investigated for the relevant problems. Among the applications of the developed methodology are fetal growth, maternal risk factors and pregnancy outcomes. A new direction for this project is to investigate statistical properties of some nonparametric procedures used for estimating the area under the receiver operating characteristic curve in the matched case-control samples.